Information on Result #734766
Linear OA(6487, 4301, F64, 31) (dual of [4301, 4214, 32]-code), using (u, u+v)-construction based on
- linear OA(6425, 199, F64, 15) (dual of [199, 174, 16]-code), using
- construction XX applied to C1 = C([59,72]), C2 = C([58,71]), C3 = C1 + C2 = C([59,71]), and C∩ = C1 ∩ C2 = C([58,72]) [i] based on
- linear OA(6423, 195, F64, 14) (dual of [195, 172, 15]-code), using the BCH-code C(I) with length 195 | 642−1, defining interval I = {59,60,…,72}, and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(6423, 195, F64, 14) (dual of [195, 172, 15]-code), using the BCH-code C(I) with length 195 | 642−1, defining interval I = {58,59,…,71}, and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(6425, 195, F64, 15) (dual of [195, 170, 16]-code), using the BCH-code C(I) with length 195 | 642−1, defining interval I = {58,59,…,72}, and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(6421, 195, F64, 13) (dual of [195, 174, 14]-code), using the BCH-code C(I) with length 195 | 642−1, defining interval I = {59,60,…,71}, and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(640, 2, F64, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(640, 2, F64, 0) (dual of [2, 2, 1]-code) (see above)
- construction XX applied to C1 = C([59,72]), C2 = C([58,71]), C3 = C1 + C2 = C([59,71]), and C∩ = C1 ∩ C2 = C([58,72]) [i] based on
- linear OA(6462, 4102, F64, 31) (dual of [4102, 4040, 32]-code), using
- construction X applied to C([0,15]) ⊂ C([0,14]) [i] based on
- linear OA(6461, 4097, F64, 31) (dual of [4097, 4036, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(6457, 4097, F64, 29) (dual of [4097, 4040, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- linear OA(641, 5, F64, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(641, s, F64, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,15]) ⊂ C([0,14]) [i] based on
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(6487, 2150, F64, 2, 31) (dual of [(2150, 2), 4213, 32]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(6487, 1433, F64, 3, 31) (dual of [(1433, 3), 4212, 32]-NRT-code) | [i] | ||